As one example for a real world application, we are use our algorithm to predict wind speed [1]}. The original measurements were observed for 24 hours from around 2pm on 1 September 2005 at about 1m above from the ground level at the Institute of Industrial Science, The University of Tokyo, Tokyo, Japan using an ultrasonic anemometer.
The original measurements were made with 50Hz, but we first sub-sample the time series using every tenth point. This sub-sampling allows us to use a longer \(L\)  and therefore the database contains more of the long term changes in the dynamics. Since we do not have access to the full state space of this environmental system, we have to reconstruct the attractor of the dynamics by using delay embedding [2]}, [3]}. Given that the system seems to have features of high-dimensional dynamics [4]}, we have to use a high dimensional embedding. But the total recording time of the wind speeds is 10,000 seconds, and consequently we cannot use too high an embedding dimension, without making the recurrence rate too low for our prediction algorithm. In addition we only use the first 9,000 seconds as our database and use the remainder for comparison with our prediction. As a compromise and after several tests, we decided to use a 10 dimensional embedding space. We find that our algorithm succeeded in capturing the large scale features of the dynamics, i.e., prolonged changes of the wind velocity are similar in the experimental data and the prediction (Fig. REF ). On the other hand our predictions fail to reproduce the finer details of the system's dynamics. We conjecture that a higher embedding dimension together with a longer time series would be able to overcome these limitations. Another way to improve the performance of the method could be to use marked spike trains, by assigning some additional value to each event. Several distances have been proposed for such marked point processes [5]}, [6]}, [7]}, [8]}, which might increase the prediction performance for such high dimensional dynamics.
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